The basis for understanding Latin, Greek, etc. roots is to help you make an educated guess at the meaning of new words you encounter.
Often, context will give you sufficient clues to guess the word's meaning, but not always. If you are familiar with roots and you can recognize the root of the new word, you can get a pretty good idea of its meaning even when there is not enough context to clearly define it, or when the context is ambiguous. Roots are especially helpful when used in conjunction with a word's context.
It also helps to know the English roots of words, so that when you come across compound words or words with crazy prefixes and suffixes you can still pretty well guess what someone is talking about.
What it means
The word pace is a Latin word, not an English word with a Latin root. For this reason, it’s usually written in italics when it occurs in an English sentence. It’s a form of pax, which is Latin for “peace”. Pace means “if so-and-so will permit” or “with deference to”, literally “with peace”.
In English, it’s a softener for very formal politeness: it means that the person you are about to name would probably disagree what what you are about say or do, but you mean no offense to that person. It’s especially appropriate when the named person has a high reputation; then it means that you don’t think that their probable error in regard to the topic at hand should detract from the respect usually given to them, which is well earned.
Examples
The example sentence from your book is not an especially good illustration of pace. It would be clearer to say “contrary to”, or even contra if you really wanted Latin for some reason. “Some Hollywood historians” is so vague, it doesn’t make much sense to say that the author means no offense to them. The point of the sentence is to contradict them, that’s all. The author probably wouldn’t say “Intending no offense to some Hollywood historians, …” or “Without tarnishing the high reputation of some Hollywood historians …” If you were going to say something like that, you would probably name the historians explicitly.
The OED gives a couple quotations where pace is very well chosen:
The color of fruit is a tacit invitation (pace the gardener) to the feast.
… Furthermore I do not believe, pace Peirce and Derrida, that it is signs all the way down, and that, pace Dennett, there is no distinctive human intentionality, and that, pace almost everyone, thinking is fundamentally linguistic. Isn’t it strange that I think so highly of [these two books by Lanham and Bolter] considering they asserted so many theses that I reject? … Nevertheless, I think these are two of the most important and culturally valuable books of the decade … [even though I disagree] on the philosophical bits. [Source]
In the first example, pace raises the possibility that finding the colors of fruit appetizing rather than beautiful for their own sake could offend the gardener—an interesting, somewhat humorous idea.
The second example comes from a review of two books, in which the reviewer explains that while he found the books illuminating with regard to their main topic (hypertext), he disagrees with their conclusions about philosophy. The point of saying pace in this passage is indicate where the reviewer’s philosophical opinions differ from those of respected authors who think in agreement with Lanham and Bolter, without getting into an argument about those topics or letting the disagreement interfere with appreciating the two books under review.
Best Answer
In my experience, gratis is not used on signs in the way that free often is.
FREE APPLES
One rarely hears gratis used in everyday speech in the US, although it is hardly unknown or unused. Gratis is above the grade-reading-level for most daily newspapers in the US.
A publisher might send a teacher a gratis copy of a book.
EDIT:As CarSmack reminds us, it can also be used as an adverb, so that the publisher could send a teacher a copy of the book gratis.